Singular scaling functions in clustering phenomena
Department of Theoretical Physics Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 400005, India
Corresponding author: a email@example.com
Revised: 4 February 2008
Published online: 9 April 2008
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size. This scaling function is singular for small argument — it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 47.40.-x – Compressible flows; shock waves / 64.75.+g – Solubility, segregation, and mixing; phase separation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008